Problem: Solve for $x$ and $y$ using elimination. ${4x-3y = -26}$ ${5x-4y = -35}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $4$ and the bottom equation by $-3$ ${16x-12y = -104}$ $-15x+12y = 105$ Add the top and bottom equations together. ${x = 1}$ Now that you know ${x = 1}$ , plug it back into $\thinspace {4x-3y = -26}\thinspace$ to find $y$ ${4}{(1)}{ - 3y = -26}$ $4-3y = -26$ $4{-4} - 3y = -26{-4}$ $-3y = -30$ $\dfrac{-3y}{{-3}} = \dfrac{-30}{{-3}}$ ${y = 10}$ You can also plug ${x = 1}$ into $\thinspace {5x-4y = -35}\thinspace$ and get the same answer for $y$ : ${5}{(1)}{ - 4y = -35}$ ${y = 10}$